Raman spectroscopic studies of proton conductors

In the next section, the theory of the Raman effect will be briefly reviewed, followed by Section 24.3, the application of Raman spectroscopy to studies of proton conductors. The description of structural information will be divided according to data obtained from band frequencies, intensities, bandwidths, and studies of phase transitions. The chapter will then conclude with several illustrations of dynamical information which can result from an appropriate analysis. 

Here Iq is the incident intensity and is the pa component of the Raman polarizability tensor originating in a transition from state j to state k. The tensor component is 

In vibrational Raman scattering, which is the primary technique of interest in studies of proton conductors, the Born approximation is invoked to write the state i as the product of an electronic wave function, e , and a vibrational wave function, d , i.e. i = k o . The subscript m on the vibrational wave function designates the mth normal vibrational mode. Usually the transition j k occurs between the vibrational level v in the ground electronic state g and the vibrational level v also in the ground electronic state, so the transition jy - k may be written Gy m + f - Here the harmonic oscillator selection rule = 

In the Placzek approximation, which is appropriate for a system with a nondegenerate electronic ground state and in which resonance does not occur, the Raman tensor is real and symmetric. 

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